Vylučování odlehlých výsledků																																																						
																																																						
																																																						
Krabicový graf a jeho dvě užití																																																						
			seřazeno		funkce =quartil.inc()																																																	
37																																																						
47																																																						
41																																																						
30																																																						
68																																																						
79																																																						
98																																																						
87																																																						
70																																																						
17																																																						
68				v krabici je....																																																		
48																																																						
65																																																						
18																																																						
86																																																						
83																																																						
82																																																						
10																																																						
84																																																						
78																																																						
29																																																						
18																																																						
83																																																						
60																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
vylučování odlehlých výsledků																																																						
metoda vnitřních hradeb																																																						
																																																						
																																																						
																																																						
7																																																						
63																																																						
110																																																						
69																																																						
87																																																						
99																																																						
62																																																						
87																																																						
89																																																						
45																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
"MVH, Vnitřní hradby, vnější hradby"																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
Která z těchto 55 hodnot je odlehlá?																																																						
																																																						
																																																						
29	179	180	201	300	301	304	350	399	401	455	501	503	540	543	549	560	561	562	563	569	570	599	601	603	650	701	703	704	709	713	733	745	801	900	982	983	985	999	1001	1002	1003	1009	1100	1101	1102	1103	1109	1201	1301	1399	1400	1501	1599	1699
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
			Q1																																																			
			Q3																																																			
			IQR																																																			
																																																						
																																																						
																																																						
																																																						
			LIF																																																			
			UIF																																																			
			LOF																																																			
			UOF																																																			
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
																																																						
						více o vylučování odlehlých výsledků - viz dále																																																
																																																						
																																																						
																																																						
																																																						
##### Sheet/List 2 #####
Která z těchto 55 hodnot je odlehlá?				 = v předchozím příkladu jsme použili MVH a vyloučili největší hodnotu 1699																																																		
				nyní použijeme Grubbsův test																																																		
																																																						
29	179	180	201	300	301	304	350	399	401	455	501	503	540	543	549	560	561	562	563	569	570	599	601	603	650	701	703	704	709	713	733	745	801	900	982	983	985	999	1001	1002	1003	1009	1100	1101	1102	1103	1109	1201	1301	1399	1400	1501	1599	1699
																																																						
	29																																																					
	179																																																					
	180																																																					
	201																																																					
	300																																																					
	301		T																																																			
	304																																																					
	350																																																					
	399																																																					
	401																																																					
	455																																																					
	501																																																					
	503																																																					
	540																																																					
	543																																																					
	549																																																					
	560																																																					
	561																																																					
	562																																																					
	563																																																					
	569																																																					
	570																																																					
	599																																																					
	601																																																					
	603																																																					
	650																																																					
	701																																																					
	703																																																					
	704																																																					
	709																																																					
	713																																																					
	733																																																					
	745																																																					
	801																																																					
	900																																																					
	982																																																					
	983																																																					
	985																																																					
	999																																																					
	1001																																																					
	1002																																																					
	1003																																																					
	1009																																																					
	1100																																																					
	1101																																																					
	1102																																																					
	1103																																																					
	1109																																																					
	1201		T																																																			
	1301																																																					
	1399																																																					
	1400																																																					
	1501																																																					
	1599																																																					
	1699																																																					
																																																						
			závěr:	V daném výběrovém souboru ....																																																		
Grubbsův test																																																						
zkontrolovat normalitu																																																						
																																																						
		 průměr																																																				
		 směrodatná odchylka																																																				
				T																																																		
	7																																																					
	63																																																					
	110																																																					
	69																																																					
	87																																																					
	99																																																					
	62																																																					
	87																																																					
	89																																																					
	45																																																					
																																																						
																																																						
																																																						
																																																						
ryby																																																						
																																																						
Rybáři vylovili malý rybník v městském parku.																																																						
"Byl to první výlov po 10ti letech, byly v něm ryby různých velikostí, celkem 30 kusů. Jejich váhy jsou tyto:"																																																						
"Zjistěte, zda-li je některá hodnota odlehlá. "																																																						
																																																						
	m (kg)	seřazeno																																																				
1	0.30			metoda vnitřních/vnějších hradeb																																																		
2	1.90																																																					
3	2.10																																																					
4	0.48				 =Q1																																																	
5	2.10																																																					
6	3.10				 =Q3 																																																	
7	0.80				 =R31																																																	
8	2.30				 =1.5*R31																																																	
9	3.20				 =3*R31																																																	
10	1.00				inner																																																	
11	1.60																																																					
12	2.20				outer																																																	
13	2.50																																																					
14	1.40																																																					
15	2.20																																																					
16	4.00																																																					
17	1.10																																																					
18	2.00																																																					
19	3.10																																																					
20	1.95																																																					
21	2.00																																																					
22	1.50																																																					
23	2.56																																																					
24	8.00																																																					
25	1.01																																																					
26	2.15																																																					
27	4.30																																																					
28	0.90																																																					
29	2.20																																																					
30	1.30																																																					
																																																						
																																																						
Dean-Dixon Q-test																																																						
																																																						
 R=																																																						
"Q1,2="																																																						
"Q29,30="																																																						
Qcrit(0.05)																																																						
																																																						
##### Sheet/List 3 #####
Najdi odlehlé hodnoty pomocí Grubbsova testu								
vyjádři interval spolehlivosti se správným počtem desetinných míst								
zaokrouhlujeme na 2 platné číslice směrodatné odchylky								
								
číslo měření	koncentrace Pb [ng/ml]		T				kritické hodnoty Grubbsova testu (dvoustranný test)	
1	37.9						N\a	0.05
2	22.8						3	1.155
3	13.4						4	1.481
4	31.6						5	1.715
5	50.8						6	1.887
6	20.2						7	2.020
7	9.5						8	2.126
8	26.7						9	2.215
9	78.1						10	2.290
10	22.0						11	2.355
							12	2.412
							13	2.462
							14	2.507
							15	2.549
							16	2.585
							17	2.620
							18	2.651
							19	2.681
							20	2.709
	sm.odchylka							
	s.e.m.							
	dolní IS							
	horní IS							
								
					normsinv			
Q-Q graf								
								
								
								
								
								
								
								
								
								
								
##### Sheet/List 4 #####
INTERVAL SPOLEHLIVOSTI - CONFIDENCE INTERVAL									
									
"Co je to interval spolehlivosti průměru? ""Confidence interval"" je oblast, kde 95% opakovaných měření nalezne skutečnou průměrnou hodnotu"									
při všech možných kombinacích výběrů z dané populace.									
									
pro opakované spojité hodnoty normálně rozdělené									
"se hodnota počítá kolem arit. průměru (""mean"")"									
příklad									
	44								
	47								
	61								
	64								
	84								
	85								
									
průměr				 =T.INV.2T(0.05;N-1)					
SEM									
CI		 =L1							
		 =L2							
									
									
									
									
									
									
pro ne-normálně rozdělené spojité hodnoty se uvádí CI kolem mediánu; 									
hledají se indexy 									
									http://perfeval.epfl.ch
									
Stanovte 95% interval spolehlivosti mediánu populace pro oba dva výběrové soubory A  a B.									
									
	species A	species B							
	16	34							
	32	36	(A) j=						
	37	38	(A) k=						
	39	45	p=						
	40	50							
	41	54							
	42	56	(B)  j=						
	50	59	(B)  k=						
	82	69	p=						
		91							
									
n=									
									
									
									
									
									
									
									
									
									
pro poměr (počty výskytů)									
Lékař vybral náhodný vzorek 215 žen ze svého registru.									
Z nich 39 trpělo astmatem. Jaký je výskyt astmatu v populaci?									
									
	celkem	n=							
		problém s astmatem=							
									
		p=							
									
		s.e.=							
				1.96					
		1/2 I.S.=							
									
		L1							
		L2							
##### Sheet/List 5 #####
příklady výpočtů intervalu spolehlivosti											
											
"V průmyslové odpadní vodě objemu 1000 ml byl polarograficky zjištěn zinek v množství: 150 μg, 142 μg, 148 μg, 134 μg, 144 μg, 140 μg, 144 μg, 139 μg, 146 μg, 139 μg, 138 μg, 146 μg. "											
"Vypočtěte směrodatnou odchylku s a interval spolehlivosti s pravděpodobností 95% (α = 0,05)."											
150	142	148	134	144	140	144	139	146	139	138	146
											
data	seřazeno	T									
											
											
											
											
											
											
											
											
											
											
											
											
											
	normálně rozděleno?										
	IS dle Studenta										
	n=										
	prumer=										
	s(n-1)=										
	t(0.05;st.v.)										
	s.e.m=										
	L1=										
	L2=										
											
											
											
	nenormálně?: indexy										
											
											
1											
2											
3											
4											
5											
6											
7											
8											
9											
10											
11											
12											
											
	L1										
	L2										
##### Sheet/List 6 #####
116.5030542	116.5		normálně rozdělená populace					0		binomicky rozdělená populace			
103.8956387	103.9		např. hladina léčiva v krvi (umol/L)					0		např. pacient lékaře s obezitou = 1			
100.3676632	100.4							1		pacient lékaře bez obezity = 0			
113.4850779	113.5							1					
102.8219347	102.8							0					
108.4581416	108.5							0					
122.1449227	122.1							0					
108.0663995	108.1							1					
114.1174496	114.1							1					
101.068031	101.1							0					
92.28657543	92.3							0					
94.85571607	94.9							0					
119.3757842	119.4							0					
112.6158284	112.6							0					
106.7350584	106.7							0					
101.5324986	101.5							0					
108.667871	108.7							0					
89.72939466	89.7							0					
129.4450729	129.4		50 náhodných čísel řádků					0		50 náhodných čísel řádků			
113.8690211	113.9							0					
120.4150638	120.4					hodnoty z B		0					hodnoty z I
93.68612862	93.7		z gen.	zaokr.celé				0		z gen.	zaokr.celé		
105.7071361	105.7					#REF!		0					#REF!
108.0103973	108.0							0					
106.7369683	106.7							1					
98.387716	98.4							1					
110.2021431	110.2							0					
90.5048071	90.5							0					
89.27955858	89.3							1					
83.95414877	84.0							0					
96.38184818	96.4							0					
94.01331934	94.0							0					
104.5437901	104.5							0					
103.0487627	103.0							0					
85.52984835	85.5							1					
90.44339347	90.4							0					
82.790996	82.8							0					
109.9204271	109.9							1					
77.95184754	78.0							0					
110.8449512	110.8							0					
100.4227786	100.4							0					
100.811383	100.8							1					
95.01226284	95.0							0					
104.9825417	105.0							0					
96.5869165	96.6							0					
100.1633339	100.2							0					
91.39323563	91.4							0					
99.45467835	99.5							0					
84.71084837	84.7							0					
84.61662472	84.6							0					
88.4714498	88.5							1					
94.76643779	94.8							0					
101.5410251	101.5							0					
94.11186309	94.1							0					
100.8843244	100.9							0					
95.42310434	95.4							0					
98.24573251	98.2							0					
106.3981361	106.4							0					
94.56890691	94.6							0					
102.254626	102.3							1					
88.42224613	88.4							1					
110.6231028	110.6							1					
96.28203113	96.3							1					
90.07081897	90.1							0					
90.06454345	90.1							0					
98.53325789	98.5							0					
104.3403134	104.3							0					
100.9319479	100.9							1					
100.2077059	100.2							0					
105.0007429	105.0							1					
110.4261289	110.4							0					
106.5708832	106.6							0					
115.7614068	115.8							0					
92.61715402	92.6							0				   počet 1	
104.7303388	104.7							0				p=	
69.29400368	69.3							1				n=	
104.2472038	104.2							0				se(p)=	
96.92959136	96.9							0					
113.7657025	113.8							0				L1	
96.80103429	96.8							0				L2	
117.8224582	117.8							0					
94.80500037	94.8							0					
99.53970473	99.5							0					
95.55437853	95.6							0					
91.39765805	91.4							1					
90.76339918	90.8				 prům			0					
101.8755941	101.9				sm.odch			1					
101.7239813	101.7				n=			1					
111.4796194	111.5				sem=			0					
85.5036549	85.5		Studentův koeficient		 =t.inv.2T			0					
104.6347395	104.6				L1			0					
86.874559	86.9				L2			0					
89.25370619	89.3							0					
103.9203996	103.9							0					
84.11017259	84.1							0					
110.9613666	111.0							0					
97.41610281	97.4							0					
97.20749884	97.2							0					
106.0747652	106.1		malý soubor			seřazeno		0					
118.5283625	118.5			1				0					
97.33454388	97.3			2				0					
98.65377731	98.7			3				1					
99.55501835	99.6			4				0					
106.5121412	106.5			5				0					
101.0518761	101.1			6				0					
110.5387471	110.5			7				1					
115.1382665	115.1			8				0					
105.1390543	105.1			9				0					
106.1661012	106.2			10				1					
90.63843461	90.6			11				0					
91.00562036	91.0							0					
104.804906	104.8				n=			0					
98.76716856	98.8				j=			1					
94.30906428	94.3				k=			1					
85.93621058	85.9							0					
92.3143605	92.3			95% IS	L1			0					
99.25536258	99.3				L2			0					
98.56881914	98.6							1					
103.6958454	103.7							0					
95.89136905	95.9							0					
111.7118816	111.7							0					
94.72340733	94.7							0					
104.5420961	104.5							0					
113.7578127	113.8							0					
107.1270506	107.1							0					
125.132249	125.1							0					
84.5891125	84.6							0					
109.7197244	109.7							0					
94.38803115	94.4							1					
79.18130248	79.2							0					
110.0793386	110.1							0					
116.2573087	116.3							0					
99.89481694	99.9							0					
119.5589564	119.6							0					
101.1357656	101.1							1					
91.16496383	91.2							1					
101.6432864	101.6							0					
112.9997716	113.0							0					
109.1653646	109.2							0					
107.3898832	107.4							0					
109.8034889	109.8							0					
95.67648956	95.7							0					
114.6400453	114.6							0					
111.4751856	111.5							0					
96.94321104	96.9							0					
105.3992153	105.4							1					
86.29323272	86.3							0					
106.1254468	106.1							0					
97.04965603	97.0							0					
95.73269633	95.7							0					
91.98960268	92.0							1					
99.72419573	99.7							0					
89.54353941	89.5							0					
101.3709268	101.4							0					
87.93455234	87.9							0					
108.8068077	108.8							0					
117.3245098	117.3							0					
91.99592366	92.0							0					
103.2650632	103.3							0					
101.3832846	101.4							1					
103.3984861	103.4							1					
90.17545633	90.2							0					
106.9750286	107.0							0					
99.84431724	99.8							0					
76.87555151	76.9							1					
114.6066213	114.6							0					
95.74945377	95.7							0					
98.66304279	98.7							0					
90.42283889	90.4							0					
89.97770945	90.0							1					
93.1415914	93.1							1					
106.6451094	106.6							0					
104.0255372	104.0							0					
85.6551085	85.7							0					
106.2012987	106.2							1					
98.52475412	98.5							0					
100.1908802	100.2							0					
100.9980454	101.0							0					
109.172345	109.2							0					
89.07203462	89.1							0					
95.83303634	95.8							0					
112.544956	112.5							0					
97.46353296	97.5							0					
112.4663529	112.5							0					
94.46933998	94.5							0					
93.61969003	93.6							0					
120.7654921	120.8							0					
85.28583092	85.3							0					
87.71950231	87.7							0					
97.93722054	97.9							0					
104.325193	104.3							0					
100.9550035	101.0							0					
89.47457698	89.5							0					
115.4840563	115.5							0					
96.7058784	96.7							0					
89.78755684	89.8							0					
101.1157454	101.1							1					
106.3990683	106.4							0					
108.5702595	108.6							0					
113.6134076	113.6							0					
97.88404921	97.9							1					
104.6961532	104.7							0					
94.11186309	94.1							0					
104.7500293	104.8							0					
93.96291059	94.0							1					
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